Minor Latex isssues in 2-D-1

_problems/unit-02/D-cdf-of-a-discrete-RV/1.md

@@ -8,7 +8,7 @@ statement: |
     3. Provide in bracket notion the cumulative distribution function (cdf) of X
     4. What are the probailities  P(X <= 2), P(X <= 1.75) and P(X >= 2.3)
 
-Problem modified afterHogg, McKean and Craig - Introduction to Mathematical Statistics     
+    Problem modified afterHogg, McKean and Craig - Introduction to Mathematical Statistics     
 ---
 Let $Y$ be a bernoulli random variable defined such that each flip
 
@@ -20,8 +20,8 @@ $$
 $$
 P(Y = y) = 
 \begin{cases} 
-0.5, &y = 0 \\
-0.5, &y = 1 \\
+0.5, &y = 0 \\\\
+0.5, &y = 1 \\\\
 0, & \text{otherwise} 
 \end{cases}
 $$
@@ -79,16 +79,15 @@ $$
 That is we sum all the mass from $\( -\infty \)$ to desired value of $x$ and recall that this cumulative probability quantity only changes at values of $X$ for which there is positive mass. Since as we recall probability is only in the range of 0 to 1, and recalling that cdf increases at increasing supp values, we have... 
 
 $$
-\(F_{X}(x) = \left\\{
-\begin{array}{ll}
-0 & \text{if } x < 0 \\
-0.0625 & \text{if } 0 \leq x < 1 \\
-0.3125 & \text{if } 1 \leq x < 2 \\
-0.6875 & \text{if } 2 \leq x < 3 \\
-0.9375 & \text{if } 3 \leq x < 4 \\
+F_{X}(x) = 
+\begin{cases}
+0 & \text{if } x < 0 \\\\
+0.0625 & \text{if } 0 \leq x < 1 \\\\
+0.3125 & \text{if } 1 \leq x < 2 \\\\
+0.6875 & \text{if } 2 \leq x < 3 \\\\
+0.9375 & \text{if } 3 \leq x < 4 \\\\
 1 & \text{if } 4 \leq x \\
-\end{array} 
-\right. \)
+\end{cases} 
 $$
 
 For part 4 we can just read off of the cdf in bracket notation